International Journal of Computer Trends and Technology (IJCTT) – volume 17 number 3 – Nov 2014

ISSN: 2231-5381 http://www.ijcttjournal.org Page 121

Analytical Comparison of Noise Reduction Filters

for Image Restoration Using SNR Estimation Poorna Banerjee Dasgupta

M.Tech Computer Science & Engineering, Nirma Institute of Technology

Ahmedabad, Gujarat, India

Abstract— Noise removal from images is a part of image

restoration in which we try to reconstruct or recover an image

that has been degraded by using a priori knowledge of the

degradation phenomenon. Noises present in images can be of

various types with their characteristic Probability Distribution

Functions (PDF). Noise removal techniques depend on the kind

of noise present in the image rather than on the image itself. This

paper explores the effects of applying noise reduction filters

having similar properties on noisy images with emphasis on

Signal-to-Noise-Ratio (SNR) value estimation for comparing the

results.

Keywords— Noise, Image filters, Probability Distribution

Function (PDF), Signal-to-Noise-Ratio (SNR).

I. INTRODUCTION

Digital images are prone to a variety of types of noise [1],[2].

Noise is the result of errors in the image acquisition process

that result in pixel values that do not reflect the true intensities

of the real scene. There are several ways in which noise can

be introduced into an image, depending on how the image is

created. For example:

If the image is scanned from a photograph made on film,

the film grain is a source of noise. Noise can also be the

result of damage to the film, or be introduced by the

scanner itself.

If the image is acquired directly in a digital format, the mechanism for gathering the data (such as a CCD detector)

can introduce noise.

Electronic transmission of image data can introduce noise.

A. Types of noises in Images

Image degradation maybe caused due to various categories of

noises such as: Gaussian, Rayleigh, Erlang, Uniform,

Exponential, Salt, Pepper, Salt-and-Pepper noises [1]. In

subsequent sections of this paper, three particular categories

of noises viz. Salt, Pepper, Salt-and-Pepper noises have been

studied and comparatively analysed through application of

various noise reduction filters. Each result has then been

qualitatively assessed with the help of SNR estimation to

determine which kind of filter is best suited for removal of a

particular noise type when there is a choice among the filters

to be used.

Salt-and-pepper noise is also known as bipolar impulse noise.

Its characteristic Probability Distribution Function (PDF) is

shown in Figure 1[1]. Bipolar impulse noise is specified as:

Here z represents intensity values of pixels in a noisy image. If

b>a, intensity b will appear as a light dot on the image and a

appears as a dark dot. If either Pa or Pb is zero the noise is

called unipolar. Frequently, a and b are saturated values,

resulting in positive impulses being white and negative impulses being black.

Fig. 1 Impulse bipolar noise

II. SNR ESTIMATION

There exist many approaches for estimation of the Signal-to-

Noise Ratio (SNR) depending on the type of data that is being analysed [3][4][5][6]. However, in the context of digital image

processing where all data values are in terms of luminance and

are positive values, the most common approach for

determining the SNR value is to take the ratio of the mean

image pixel intensity values () and the standard deviation of

the image pixel values (), i.e. SNR = In subsequent sections of this paper, this approach for SNR estimation has

been used for qualitative analysis and comparison of the

outputs of noise reduction filters – higher SNR values are

indicative of better noise removal.

International Journal of Computer Trends and Technology (IJCTT) – volume 17 number 3 – Nov 2014

ISSN: 2231-5381 http://www.ijcttjournal.org Page 122

III. COMPARISON OF NOISE REDUCTION FILTERS

In this section, a comprehensive comparative study of noise

reduction filters with input test images has been carried out.

The results and findings of the study have been summarized in

Tables 1 to 3. The original, noise-free input test image is

shown in Figure 2 [1]

. For the original, noise-free image, the

following statistics were obtained:

SNR

Fig. 2 Original noise-free image

A. Removal of Salt Noise

Filters used for noise reduction:

- Min Filter

- Contra-harmonic mean filter (CHM) The resultant images are shown below. Figure 3(a) shows the

input test image with salt noise [1]. Figure 3(d) shows the

output after applying a 3x3 Min filter and Figure 3(e) shows

the result of subtracting this output from the input test image.

Figure 3(b) shows the output after applying Contra-harmonic

mean filter with Q-parameter = -1 and Figure 3(c) shows the

result of subtracting this output from the input test image.

These subtracted images show an estimate of how close the

output is with the input image and also the amount of noise

removed from the image. SNR values were calculated for each

output and the following results were obtained as shown in Table 1.

TABLE I

SNR FOR SALT-NOISE REDUCTION FILTERS

SNR of input

noisy image

SNR of Min

Filter’s

output

SNR of CHM

Filter’s output

SNR = 9.6

SNR8.5

SNR7.6

Fig 3(a) Input image with salt noise

Fig 3(b) Output of CHM Filter Fig 3(c) Input minus Output of

CHM Filter

Fig 3(d) Output of Min Filter Fig 3(e) Input minus Output of Min

Filter

Due to presence of salt noise in the image, the mean value

comes to be quite high. However, after applying the filters, it has been found that the Min filter yields a better result and a

closer SNR value to that of the original noise-free image. Also

it was noticed that applying Contra-harmonic mean filters

leads to undesirable thickening of dark areas in the image.

This is especially noticeable for the pins in the figure of the

circuit diagram.

B. Removal of Pepper Noise

Filters used for noise reduction: - Max Filter

- Contra-harmonic mean filter (CHM) The resultant images are shown below. Figure 4(a) shows the

input test image with pepper noise [1]. Figure 4(b) shows the output after applying a 3x3 Max filter and Figure 4(c) shows

International Journal of Computer Trends and Technology (IJCTT) – volume 17 number 3 – Nov 2014

ISSN: 2231-5381 http://www.ijcttjournal.org Page 123

the result of subtracting this output from the input test image.

Figure 4(d) shows the output after applying Contra-harmonic

mean filter with Q-parameter = +1 and Figure 4(e) shows the

result of subtracting this output from the input test image.

SNR values were calculated for each output and the following

results were obtained as shown in Table 2.

TABLE II

SNR FOR PEPPER-NOISE REDUCTION FILTERS

SNR of input

noisy image

SNR of Max

Filter’s

output

SNR of CHM

Filter’s output

SNR16.4

SNR10.2

SNR

Fig 4(a). Input image with pepper noise

Fig 4(b) Output of Max Filter Fig 4(c). Output of Max Filter minus

Input

Fig 4(d). Output of CHM Filter Fig 4(e). Input minus Output of CHM

Filter

Due to presence of pepper noise in the image, the mean value

comes to be lower than that of the original noise-free image.

However, after applying the filters, it has been found that the

Max filter yields a better result and a closer SNR value to that

of the original noise-free image. Also it was noticed that

applying Contra-harmonic mean filters leads to a higher SNR

value but also produces an undesirable “washed-out” effect.

C. Removal of Salt-and-Pepper Noise

Filters used for noise reduction:

- Static Median Filter (SMF)

- Adaptive Median Filter (AMF)

The resultant images are shown below. Figure 5(a) shows the

input noisy test image [1]. Figure 5(b) shows the output after

applying a 3x3 Static Median filter and Figure 5(c) shows the

result of subtracting this output from the input test image.

Figure 5(d) shows the output after applying Adaptive Median

filter with maximum allowable filter size of 5x5 and Figure 5(e) shows the result of subtracting this output from the input

test image. SNR values were calculated for each output and

the following results were obtained as shown in Table 3.

TABLE III

SNR FOR SALT-PEPPER NOISE REDUCTION FILTERS

SNR of input

noisy image

SNR of Static

Median Filter’s

output

SNR of Adaptive

Median filter’s

output

SNR.7

SNR.7

SNR7

Fig 5(a) Input image with salt and pepper noise

Fig 5(b) Output of SMF Fig 5(c) Input minus Output of SMF

International Journal of Computer Trends and Technology (IJCTT) – volume 17 number 3 – Nov 2014

ISSN: 2231-5381 http://www.ijcttjournal.org Page 124

Fig 5(d) Output of AMF Fig 5(e) Input minus Output of AMF

Due to presence of both pepper and salt noise in the image,

the mean value comes to be quite close to that of the original

noise-free image. However, after applying the filters, it has

been found that the Static Median filter yields a better result

and a closer SNR value to that of the original noise-free image.

Also it was noticed that applying Adaptive Median filters leads to a higher SNR value but also produces undesirable

black boundaries if zero-padding is used for border pixels.

Also it is more time consuming than applying Static Median

filters. However using Adaptive Median Filters help preserve

edges better which are a part of the original image.

IV. CONCLUSIONS & FUTURE SCOPE OF WORK

Noises present in images can be of various types with their characteristic probability distribution functions. Noise

removal techniques depend on the kind of noise present in the

image rather than on the image itself. This paper explored the

effects of applying noise filters having similar effects on noisy

images with emphasis on SNR value estimation for comparing

the results. Three categories of noises were analysed viz. Salt

noise, Pepper noise and Salt-&-Pepper noise. For each type of

noisy image, different filters were applied for noise removal

and the filter outputs were then qualitatively assessed using

SNR values of each output.

As further extensions to the research work carried out in this paper, more filters can be analysed for other categories of

noises and other quality parameters such as edge restoration in

images can be used to assess the filter outputs. Also the

analysis can be further extended to color images as well.

REFERENCES

[1] Rafael C. Gonzalez ,Richard E. Woods. Digital Image Processing, 3rd

Edition, Prentice Hall Publications, 2000.

[2] Peter Kellman, Elliot R. McVeigh. Image reconstruction in SNR units:

A general method for SNR measurement. Wiley Publications, 2005.

[3] John C. Russ. The image processing handbook. 5th

Edition CRC

Press,2007.

[4] Suk Hwan Lim ; Maurer, R. ; Kisilev, P. “Denoising scheme for

realistic digital photos from unknown sources”. IEEE International

Conference on Acoustics, Speech and Signal Processing, 2009.

[5] D. J. Schroeder. Astronomical Optics ,2nd Edition, Academic Press,

1999.

[6] Tania Stathaki. Image fusion: algorithms and applications. Academic

Press, 2008.

AUTHOR’S PROFILE: Poorna Banerjee Dasgupta has received

her B.Tech & M.Tech Degrees in Computer

Science and Engineering from Nirma

Institute of Technology, Ahmedabad, India.

She did her M.Tech dissertation at Space

Applications Center, ISRO, Ahmedabad,

India and has also worked as Assistant Professor in Computer

Engineering dept. at Gandhinagar Institute of Technology,

Gandhinagar, India from 2013-2014. Her research interests

include image processing, high performance computing,

parallel processing and wireless sensor networks.